Didn't know it was an LFA?
Isn't that why one employs solicitors to carry out the necessary searches and the requirement for the vendor to exercise due dilligence in declaring matters that affect the property and its environs?
Get a better solicitor - one with local knowledge...
BTW - I live in the Lake District and revel at seeing all manner of aircraft transiting at snot feet. The locals don't even notice them - it's the 'Beatrix Potter' or the 'knobbly-kneed' cagoul-wearers tourists that complain.